A recurve blade has an edge that curves inward toward the handle before sweeping back out toward the tip, producing an S shape. The concave section pulls material in and cuts aggressively, at the cost of being much harder to sharpen.
The inward curve acts like a shallow hook. Material sliding along the edge gets drawn into the concave section rather than pushed off the front, so the blade bites into rope, vegetation and fibrous material that a straight edge would skate over.
It also increases total edge length within the same blade length, which is a real benefit for chopping tools like machetes and kukris.
A flat stone cannot reach the inside of the concave section. Trying anyway flattens the recurve out over time and eventually destroys the profile.
You need a round rod, the narrow edge of a stone, or a slack belt. Budget for that before buying a recurve, because a recurve you cannot sharpen is a recurve you will stop carrying. See hawkbill for the more extreme version of the same issue.